International Journal of Science and Research (IJSR)
ISSN: 2319-7064
ResearchGate Impact Factor (2018): 0.28 | SJIF (2018): 7.426
Volume 8 Issue 6, June 2019
www.ijsr.net
Licensed Under Creative Commons Attribution CC BY
Case 1 : If
,
17
22
1
sec
2
3
,2
ctx
c
c
h
c
txU
Case 2 : If
,
18
22
1
sec
2
3
,2
ctx
c
cc
txU
It is clear that in case1, the set of exact solution of the
general form of BBM are solitary waves having the
profile
. Hence, we have soliton-type solutions. On
the other hand, case2 gives us solutions of the type
compactons with the profile
. Which clearly are not
solitons.
4. Conclusion
As a conclusion, we used the Hopf-Cole transformation [10]
to linearize Benjamin-Bona-Mahony's pseudo-parabolic
nonlinear generalized equation, and we obtained a suitable
form for determining a solution that was difficult to get in
the past. In addition, it is appropriate to note the ease of the
method, which offers a solution with the soliton profile. We
have also presented a comparative analysis of the results
obtained using the functional variable method [11]-[12], and
we note that solutions are visibly very close. Even if, we
have used two different methods, results are fascinating.
5. Acknowledgement
We would like to thank the Ordinary Professor Walo Omana
Rebecca for her considerable contribution throughout the
development of this text.
References
[1] T. B. Benjamin, J.L. Bona, and J. J. Mahony, “Model
equations for long waves in nonlinear dispersive
systems”, Philosophical Transactions Royal Society of
London. Series A, vol. 272, NO 1220, pp 47-78, 1972
[2] H.Zhang,G.M.Wei and Y.T.Gao , “on the general form
of the Benjamin-Bona-Mahony equation in fluid
mechanics”, czechoslovak journal of physics,
vol.51,NO.3,pp. 373-377, 2001
[3] Jacek Dziubanski and Grzegirz Karch, Wroclan ,
“nonlinear scattering for some dispersive equations
generalizing Benjamin-Bona-Mahony”, Mh. Math.122,
pp. 35-43, 1996
[4] H.Gündogdu and O.F. Gözükizil , “solving Benjamin-
Bona-Mahony equation by using the sn-sn method and
the tanh-coth methode”, mathematica MORAVICA,
vol.21, NO.1, pp. 95-103, 2017
[5] Muhammmad Ikram, Abbas Muhammad, Atiq Ur
Rahm , “ Analytic solution to Benjamin-Bona-Mahony
equation by using Laplace Adomian decomposition
method”, Matrix Science Mathematic, 3(1) :pp. 01-04,
2019
[6] A.El Achab, A.Bekir , “travelling wave solutions to
generalized Benjamin-Bona-Mahony (BBM)”,
international journal of nonlinear science, vol.19
NO.1,pp.40-46, 2015
[7] A.M.Wazwaz , “ nonlinear variants to the BBM
equation with compact and non-compact physical
structure”, Chaos, solitons and fractals, 26 : pp.767-
776,2005
[8] Ben Muatjetjeja and Massod Khalique , “Benjamin-
Bona-Mahony equation with variable coefficients :
conservation laws”, symmetry,6, pp.1026-1036, 2014
[9] Gözükizil and Akçagil , “ Exact solutions of Benjamin-
Bona-Mahony-Burgers-Type non linear pseudo-
parabolic equations”, Boundary Value Problems 2012
pp. 144, 2012
[10] Lawrence C.Evans, “ Partial Differential Equations,
Graduate studies in Mathematics”, volume 19,
American Mathematical society, pp.194-195, 1997
[11] A. Zerarka, S.Ouamane, A.Attaf , “On the functional
variable method for finding exacts solutions to a class
of wave equations”, applied mathematics and
computation 217 , pp. 2897-2904, 2010
[12] A. Zerarka, S.Ouamane , “Application of functional
variable method to a class of nonlinear wave
equations”, world journal of modelling and simulation
vol.6 NO.2,pp.150-160, 2010
[13] O.Asayyed, H.M.Jaradat, M.M.M. jaradat, Zead
Mustafa, Feras Shatat , “Multi-Solutions of BBM
equation arisen in shallow water”, Journal Of
Nonlinear Science And Application, 9,pp 1807-1814,
2016
Author Profile
R.Gilles Bokolo is born in Laxou (France). He
received the B.S. and M.S. degrees in Applied
Mathematics from the University of Kinshasa in 2010
and 2019, respectively. During 2010-2019, he
worked as Relationship Manager Support at
Citigroup DRC and in the Credit Department of Standardbank.
Alumni of the International Visitor Leadership Program (IVLP) of
the US State Department, he now keep working as Teaching
Assistant in the Department of Mathematics and Computer
Sciences of the University of Kinshasa, to supervise Analysis 2,
complex analysis and Ordinary Differential Equations.
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